Spring 2024
Time & Location: All talks are on Tuesdays in TBA at 3:30PM unless otherwise noted.
Organizer: Sang-Eun Lee
January 30
Title: Student Activities in Mathematics at Tulane
Sang-Eun Lee - Tulane University
Abstract: We will wrap up the activity we did last semester and propose this semester's events.
Time: 3:30 pm
Location: Gibson Hall 126
February 6
Title: Rigid Microspheres in a Stokes Fluid: Motion Due to White Noise
Irene - Tulane University
Abstract: This talk will center around the dynamic behavior of small spherical particles subjected to externally applied random forces while immersed in a viscous fluid. In contrast to the stochastic immersed boundary method which averages fluctuating random forces within the particle location, here, these forces are in the surrounding fluid, external to the particle surfaces.
Time: 3:30 pm
Location: Gibson Hall 126A
February 6
Mardi Gras
February 20
Title: Statistical Phylogenetic Approach to Characterize the Evolutionary Impact of Interlocus Gene Conversion (IGC)
Yufei - Tulane University
Abstract: Interlocus Gene Conversion (IGC) is a type of mutation that homogenizes repeated DNA sequences. Although substantial progress has been made with regard to inferring nucleotide substitutions that result from point mutations, IGC has typically been ignored when the genomes of related species are studied. This can potentially lead to misleading inferences about evolutionary history and process. Here we apply a composite likelihood approach to IGC inference. By applying this approach to data sets from segmentally-duplicated regions of primates, our results show that evolutionary changes from IGC occur at substantially different rates in different segmentally-duplicated regions.
Time: 3:30 pm
Location: Gibson Hall 126A
February 27
Title: Inverse PDE Problem: Comparison Between Numerical Method and Physics-informed Neural Network
Lan Trinh | Tulane University
Abstract: In our problem, we’re interested in the number of particles inside biological cells, which is governed by a Poisson spatial process with the intensity measure u(x). This u(x) is shown to satisfy a PDE with two unknown parameters z (source location) and lambda (nondimensional quantity) constructed from the diffusivity constant, emerging rate, and size of the cell. We also let u(x) equal 0 on the domain's boundary U, assuming that the particles are absorbed once hitting it. In this talk, I will discuss a simple version of this model in the 1D case using two methods: finite difference technique and Physics-informed Neural Network, then discuss the advantages, disadvantages as well as a potential combination of these methods for the full model in the 2D case.
Time: 3:30 pm
Location: Gibson Hall 126
March 5
Title: Intro to Continued Fractions
Peter - Tulane University
Abstract: Continued fractions are representations of real numbers that use infinitely nested fractions, in contrast to decimal representations which use infinite sums. They provide excellent rational approximations and don't require choosing a base beforehand, which are benefits over decimal representations. However, there are issues of convergence and uniqueness which need to be addressed. I will discuss this as well as more examples and properties of continued fractions.
Time: 3:30 pm
Location: Gibson Hall 126
March 12
Title: A few non-classical time stepping methods to study fluid flow problems at low Reynolds number
Moslem - Tulane University
Abstract: Very often the dynamics of a system mimicking real-world phenomena seem to be well modeled by a system of ordinary differential equations. In practice, it's nearly impossible to solve such systems analytically, and this is why lots of efforts have been made to approximate those numerically. Usually, explicit methods(those that require knowledge from previous steps only) are very popular due to less computational effort required. However, those methods tend to return unstable solutions(the solution becomes unbounded in finite time). In this talk, I'll try to review a few non-explicit time integrators with the intention reduce the level of this type of shortcoming considering an example emerging from fluid flow governed by Stokes' equation.
Time: 3:30 pm
Location: Gibson Hall 126
March 19
Title: Geometric Realization: How to add shape to otherwise shapeless data sets
Will - Tulane University
Abstract: We will learn how to add shape to data sets, even when those sets are not necessarily plottable or graphable in n-dimensional real space. Then, we’ll learn what the shape of our data sets could tell us about our data.
Time: 3:30 pm
Location: Gibson Hall 126
April 2
Title: TBA
Sinchita - Tulane University
Abstract: TBA
Time: 3:30 pm
Location: Gibson Hall 126
April 9
Title: Rees algebra of graded families of Newton-nondegenerate ideals
Vinh - Tulane University
Abstract: In commutative algebra, if we have an algebra, one of the natural questions is if the algebra is Noetherian. The Noetherian property means that the algebra is finitely generated. It is a significant property because many commutative algebra results require or relate directly to the algebras' finiteness such as Hibert's fourteen problem. Now, given a graded family of ideals, we can consider the Rees algebra of this family. In this talk, we want to introduce the definition and basic properties of a special class of ideals called Newton-nondegenerate ideals and characterize the Noetherian property of the Rees algebra of a graded family of Newton-nondegenerate ideals using the concept of Newton-polyhedron.
Time: 3:30 pm
Location: Gibson Hall 126A
April 16
Title: On the zeros of a special family of Jacobi polynomials with non-classical parameters.
John Jairo Lopez Santander | Tulane University
Abstract: The distribution of zeros of orthogonal polynomials plays a pivotal role in various mathematical analyses. In particular, classical Jacobi polynomials, denoted as p_n(x;a,b), where both a and b are greater than -1, are well-known for having all their zeros confined within the interval (-1, 1) due to orthogonality properties on this interval. However, when either parameter a or b deviates from this classical range, the zeros may migrate into the complex plane, as orthogonality on the interval is no longer guaranteed. In this talk, we will explore a specific family of Jacobi polynomials with varying non-classical parameters and discuss a related Riemann-Hilbert Problem to investigate the distribution of their zeros.
Time: 3:30 pm
Location: Gibson Hall 126
April 23
Title: An introduction to Algebraic Coding Theory
Dillon - Tulane University
Abstract: Coding theory has many tools that come from Algebra and Algebraic Geometry. We will explore some of the important families of error-correcting codes that are used today.
Time: 3:30 pm
Location: Gibson Hall 126
